On an integral-type operator from Privalov spaces to Bloch-type spaces

Volume 101 / 2011

Xiangling Zhu Annales Polonici Mathematici 101 (2011), 139-147 MSC: Primary 47B38; Secondary 30D45. DOI: 10.4064/ap101-2-4

Abstract

Let $H(B)$ denote the space of all holomorphic functions on the unit ball $B$ of ${\mathbb C}^n$. Let $\varphi$ be a holomorphic self-map of $B$ and $g \in H(B)$ such that $g(0)=0$. We study the integral-type operator $$ C_\varphi^g f(z)= \int_0^1 \Re f(\varphi(tz)) g(tz)\,\frac{dt}{t}, \ \quad f \in H(B). $$ The boundedness and compactness of $C_\varphi^g$ from Privalov spaces to Bloch-type spaces and little Bloch-type spaces are studied

Authors

  • Xiangling ZhuDepartment of Mathematics
    JiaYing University
    514015, Meizhou, GuangDong, China
    e-mail

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